| Title:
|
$(L,\varphi)$-representations of algebras (English) |
| Author:
|
Walendziak, Andrzej |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
135-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the concept of an $(L, \varphi )$-representation of an algebra $A$ which is a common generalization of subdirect, full subdirect and weak direct representation of $A$. Here we characterize such representations in terms of congruence relations. (English) |
| Keyword:
|
finitely restricted subdirect product |
| Keyword:
|
full subdirect product |
| Keyword:
|
weak direct product |
| Keyword:
|
congruence lattice |
| Keyword:
|
distributivity |
| MSC:
|
08A05 |
| MSC:
|
08A30 |
| MSC:
|
08B26 |
| idZBL:
|
Zbl 0796.08002 |
| idMR:
|
MR1263114 |
| . |
| Date available:
|
2008-06-06T21:24:22Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107475 |
| . |
| Reference:
|
[1] Crawley, P., Dilworth, R .P.: Algebraic theory of lattices.Prentice-Hall, Englewood Cliffs (N.J.), 1973. |
| Reference:
|
[2] Draskovičová, H.: Weak direct product decomposition of algebras.In: Contributions to General Algebra 5, Proc. of the Salzburg Conference (1986), Wien (1987), 105-121. MR 0930914 |
| Reference:
|
[3] Hashimoto, J.: Direct, subdirect decompositions and congruence relations.Osaka Math. J. 9 (1957), 87-112. Zbl 0078.01805, MR 0091248 |
| Reference:
|
[4] Jakubík, J.: Weak product decompositions of discrete lattices.Czech Math. J. 21(96) (1971), 399-412. MR 0286723 |
| Reference:
|
[5] McKenzie, R., McNulty, G., Taylor, W.: Algebras, Lattices, Varieties.Volume I, California, Monterey, 1987. MR 0883644 |
| . |
